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Sequences
Polynomials and Factoring
Quadratics
Radicals
Rationals
100
What is the common difference of this sequence? 4,-1,-6,-11...
-5
100
Put the polynomials in standard form and name them by the degree and number of terms. (Two parts) x+8x³-3x⁷ and 6x²-13x²-4x+4
-3x⁷+8x³+x 7th degree trinomial, -7x²-4x+4 quadratic trinomial
100
Identify the vertex of the equation f(x)=3x²-6x+1.
(1,-2)
100
If a right triangles's legs measure 10 inches and 24 inches, what is the length of its hypotenuse?
26 inches.
100
Simplify and identify restrictions: (10c+c²-3c³)/(5c²-6c-8)
[-c(3c+5)]/(5c+4) c≠-4/5 or 2
200
Is this sequence geometric or arithmetic? Explain why. -4,-1,2,5...
It is arithmetic because there is a common difference of 3.
200
What is (x³-3x²+5x)-(7x³+5x²-12)?
-6x³-8x²+5x+12
200
Solve 4x²-21x=18 by factoring.
x=6,-3/4
200
Simplify √(5)[√(81/49)]
[9√(5)]/7
200
Simplify and find restrictions (Two parts): [(4x+12)/(x²-2x)][x/(6x+18)], (3d²+2d-29)÷(d+3)
2/[3(x-2)] x≠2,-3, 3d-7-8/(d+3) d≠-3
300
Write the recursive and explicit formula for the arithmetic sequence: -3,1,5,9...
Recursive: aₙ=aₙ₋₁+4, Explicit: aₙ=-3+4(n-1)
300
Multiply (Three parts): (x+3)(2x-7), (x-4)², (3x²+x-5)(2x-7)
2x²-x-21, x²-8x+16, 6x³-19x²-17x+35,
300
Solve 2x²+16x-32=0 by completing the square.
x=-4±4√(2)
300
Simplify so that it has only only positive exponents for the variables: [4√(36x²y³z⁴)]/[6√(11)+9√(11)]
[8√(11)xz²y⁵/²]/55
300
Simplify and find the restrictions: 9/(3x-1)-5x/(2x+3)
(-15x²+23x+27)/[(3x-1)(2x+3)] x≠1/3, -3/2
400
Write the recursive and explicit formula for the geometric sequence: 8,-4,2,-1...
Recursive: aₙ=aₙ₋₁∗(-1/2), Explicit: aₙ=8(-1/2)ⁿ⁻¹
400
Factor (Four parts): 5x²+11x+2, 3x²+4x-15, x²-4x+4, 81x²-1
(x+2)(5x+1), (3x-5)(x+3), (x+2)², (9x+1)(9x-1)
400
Convert f(x)=5x²+30x+41 to vertex form.
f(x)=5(x+3)²-4
400
Solve 2y=√(5y+6).
y=2 (-3/4 is an extraneous solution.)
400
s/(3s+2)+(s+3)/(2s-4)=-2s/(3s²-4s-4)
s=-6/5, -1, s≠2,-2/3
500
A certain culture of yeast increases by 50% every three hours. A scientist places 9 grams of the yeast in a culture dish. Is this geometric or arithmetic? Write an explicit formula for this situation. How much yeast will there be after 9 hours?
It is geometric. The rule is aₙ=9(1.5)ⁿ⁻¹ After 9 hours, there will be 30.375 grams of yeast.
500
Factor x⁴+2x³-9x²-18x completely
x(x+3)(x-3)(x+2)
500
Use the quadratic formula to solve 3x²+10x-7=0.
[-5±√(46)]/3
500
The population of a town is modeled by the function p=25√(3t)+2000, where p is the population and t is the time since 2000. What is the population in 2007?
The population is about 2115 people.
500
Mike can bake a batch of cookies in 40 minutes. Sarah can do the same in one hour. If they work together, how long will it take them to bake one batch of cookies?
24 minutes